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lieven lebruyn
1,527 followers -
mathematician by day, blogger by night
mathematician by day, blogger by night

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Nice Quanta-article on the cosmic Galois group.

Here's the arXiv paper by Francis Brown on which it is based:
https://arxiv.org/abs/1512.06409
Here's some info about the cosmic group at the nLab:
https://ncatlab.org/nlab/show/cosmic+Galois+group
And an older arXiv note by Jack Morava:
https://arxiv.org/abs/1108.4627

Quanta: "Brown is looking to prove that there’s a kind of mathematical group — a Galois group — acting on the set of periods that come from Feynman diagrams. “The answer seems to be yes in every single case that’s ever been computed,” he said, but proof that the relationship holds categorically is still in the distance. “If it were true that there were a group acting on the numbers coming from physics, that means you’re finding a huge class of symmetries,” Brown said. “If that’s true, then the next step is to ask why there’s this big symmetry group and what possible physics meaning could it have.”

Among other things, it would deepen the already provocative relationship between fundamental geometric constructions from two very different contexts: motives, the objects that mathematicians devised 50 years ago to understand the solutions to polynomial equations, and Feynman diagrams, the schematic representation of how particle collisions play out. Every Feynman diagram has a motive attached to it, but what exactly the structure of a motive is saying about the structure of its related diagram remains anyone’s guess."

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The Hallucinated Stacks Project

Andrej Karpathy has a nice blog post on "The Unreasonable Effectiveness of Recurrent Neural Networks" [1]. He gives examples of how such networks can deal with Shakespeare, Wikipedia, Linux source code, baby names and... algebraic geometry!

here's what you can expect when you feed a recurrent neural network the entire Stacks project [2]. 

"We downloaded the raw Latex source file (a 16MB file) and trained a multilayer LSTM. Amazingly, the resulting sampled Latex almost compiles. We had to step in and fix a few issues manually but then you get plausible looking math, it's quite astonishing:"

about what you might expect of an unguided student who stumbles upon the project. they might be slightly better at hallucinating plausible diagrams though...

[1] : http://karpathy.github.io/2015/05/21/rnn-effectiveness/

[2] : http://stacks.math.columbia.edu/

via reddit/m
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where are the videos of the Grothendieck conference?

Mid june 2015 a conference "Mathematics of the 21st century: the vision of Alexander Grothendieck'' was held in Montpellier [1]. In a comment to a post here on Maltsiniotis' talk [2] i mentioned that most of the talks were video-taped and that they would soon be made public.

When they failed to surface on the Montpellier website, i asked +Damien Calaque  for more information. Some months ago Damien told me the strange (and worrying) tale of their fate.

At that moment Damien was in a process of trying to recover the videos. Two weeks ago he told me things were looking good, so i now feel free to post about it.

Michael Wright is the head of the Archive for Mathematical Sciences & Philosophy [3]. He arranged with the organizers of the conference that he would send someone over to video-tape the lectures and that he would make them available on his Archive. He also promised to send a copy of the videos to Montpellier, but he never did. Nor did the tapes appear on his site.

Damien Calague emailed Wright asking for more information and eventually got a reply. It appears that Wright will not be able to edit the videos nor put them online in a reasonable time.

They agreed that Damien would send him a large capacity USB-drive. Wright would copy the videos on it and send it back. Damien will arrange for the videos to be edited and the University of Montpellier will put them online. Hopefully everything will work out smoothly.

So please keep an eye on the website of l'Institut Montpelliérain Alexander Grothendieck: http://www.i3m.univ-montp2.fr/

[1] : http://www.i3m.univ-montp2.fr/grothendieck-2015
[2] : https://plus.google.com/u/0/+lievenlebruyn/posts/2L5wgoQFgLK
[3] : http://www.archmathsci.org/
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Psst : the 49th Mersenne prime was discovered 12 days ago. 

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I just love Woit's final paragraph:

"I’m actually in a way more sympathetic than most people to the idea that “non-empirical” evaluation of a theory is an important and worthwhile topic. Fundamental physics theory is facing a huge problem due to the overwhelming success of the Standard Model and the increasing difficulty of exploring higher energy scales. If it is to continue to make progress there is a real need to do a better job of evaluating theoretical ideas without help from experiment. There is a group of scientists who have a lot of experience with this problem, and have a well-developed culture designed to deal with it. They’re called “mathematicians”. Despite the fact that this workshop is hosted by the Munich Center for Mathematical Philosophy, the organizers don’t seem to have thought it worthwhile to invite any mathematicians or mathematical physicists to participate, missing out on a perspective that would be quite valuable."

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Did Chevalley invent the Zariski topology?

In his inaugural lecture at #ToposIHES Pierre Cartier stated (around 44m11s):
"By the way, Zariski topology, as we know it today, was not what Zariski invented. He invented a variant of that, a topology on the set of all valuation rings of a given field, which is not exactly the same thing. As for the Zariski topology, the rumour is that it was invented by Chevalley in a seminar given by Zariski, but I have no real proof."
Do you know more about this?

Btw. the full lecture of Cartier (mostly on sheaf theory) is not on the IHES YouTube channel, but on the channel of +Laurence Honnorat:
https://www.youtube.com/watch?v=OeGj6JqiyHk

The IHES did begin to upload videos of the remaining plenary talks at
https://www.youtube.com/channel/UC4R1IsRVKs_qlWKTm9pT82Q/videos (so far, the wednesday talks are availble).

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Proud to be working at a well-known university
First time I'm mentioned in "Nature", they issue this correction:
Corrected: An earlier version of this story incorrectly located the University of Antwerp in the Netherlands. It is in Belgium. The text has been updated.

Not particularly proud of the quote they took from my blog though:

“Is it just me, or is Mochizuki really sticking up his middle finger to the mathematical community”.

In celebration, i've put that 'lost' post back online (for now):
http://goo.gl/yUB72Y

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Maltsiniotis' talk on Grothendieck's Lasserre-gribouillis   #Grothendieck

Yesterday, George Maltsiniotis gave a talk at the Gothendieck conference in Montpellier with title "Grothendieck's manuscripts in Lasserre" [1].

This morning, +David Roberts  asked for more information on its content, and earlier i gave a short reply on what i learned [2], but perhaps this matter deserves a more careful write-up.

+Damien Calaque  attended George's talk and all info below is based on his recollections. Damien stresses that he didn't take notes so there might be minor errors in the titles and order of the parts mentioned below.

EDIT: based on info i got from +Pieter Belmans  in the comments below (followed up by the picture he got via +Adeel Khan  taken by Edouard Balzin) i've corrected the order and added additional info.

 The talk was videotaped and should become public soon.

As i mentioned last week [3] Grothendieck's family has handed over all non-family related material to the Bibliotheque Nationale. Two days ago, Le Monde wrote [4] that the legacy consists of some 50.000 pages.

Maltsiniotis insisted that the BNF wants to make these notes available to the academic community, after they made an inventory (which may take some time).

I guess from the blackboard-picture i got from Pieter, the person responsible at the BNF is Isabelle le Masme de Chermont [7].

The Lasserre-griboillis themselves consists of 5 parts:

1. Géométrie élémentaire schématique. (August 1992)
This is about quadratic forms and seems to be really elementary.

2. Structure de la psyché. (12/10/1992-28/09/1993) 3600 pages
This one is about some combinatorics of oriented graphs with extra-structure (part of the structure are successor and predecessor operators on the set of arrows).

3. Psyché et structures (26/03/93-20/06/93) 700 pages
This one is non-mathematical.

4. Maxwell equations.
Maltsiniotis mentioned that he was surprised to see that there was at best one mathematics book in G's home, but plenty of physics books.


5. Le problème du mal. (1993-1998) 
This one is huge (30.000 pages) and is non-mathematical.

Note that also the Mormoiron-gribouillis will be made public by the University of Montpellier, [5] or if you prefer video [6].

Finally, is the photo below what you think it is? Yep!

[1] : http://www.i3m.univ-montp2.fr/files/COMM/GROTHENDIECK/GROTHENDIECK2015schedule.pdf
[2] : https://plus.google.com/+DavidRoberts/posts/Nn5CxhFudrZ
[3] : https://plus.google.com/+lievenlebruyn/posts/eUikTH73JBg
[4] : http://www.lemonde.fr/sciences/article/2015/06/17/des-milliers-de-manuscrits-du-genie-des-maths-alexandre-grothendieck-bientot-numerises_4656174_1650684.html
[5] : http://www.liberation.fr/sciences/2015/06/17/les-gribouillis-d-alexandre-grothendieck-enfin-sauvegardes_1331465
[6] : http://france3-regions.francetvinfo.fr/languedoc-roussillon/2015/06/17/les-notes-manuscrites-d-alexander-grothendieck-seront-archivees-montpellier-750077.html
[7] : http://www.bnf.fr/documents/organigramme.pdf
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Grothendieck's later writings   #Grothendieck

Next week there's a Grothendieck conference at Montpellier http://goo.gl/dAJGoR. George Maltsiniotis will give a talk thursday afternoon with the  exciting title "Grothendieck's manuscripts in Lasserre" (hat tip +Pieter Belmans ).

You may recall that G's last hideout was in the Pyrenean village of Lasserre  https://goo.gl/MyDGH3.

After a bit of sleuthing around I've heard some great news.

Grothendieck's family have donated all of his later writings (apart from his correspondences and other family-related stuff) to the Bibliotheque Nationale. The BNF have expressed their intention of scanning all this material (thousands of pages it seems) and making them (eventually) available online!

Rumour has it that the donation consists of 41 large folders containing G's reflections, kept in the form of a diary (a bit like 'Clef des Songes' http://goo.gl/pdy0q8), on G's usual suspects (evil, Satan, the cosmos), but 2 or 3 of these folders contain mathematics (of sorts).

Probably, Maltsiniotis will give a preview on this material. To anyone lucky enough to be able to go down south next week and to attend his talk, please keep me in the loop...
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wOZ declares 2015 mathematically sound!

“2015 is mathematically sound.
20 is 4*5 and 15 is 3*5. 2015 is 5*13*31. 13 and 31 are reversed digit prime numbers.
In binary 2015 is 11111011111, a palindrome.
2015 is also 3737 in base 8 (octal) and 37 is the most special number of all in my opinion. For one thing, it’s the best age. For another, it’s the first irregular prime number!"

a math-happy 2015 :: lieven.
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